Physics 1501: Lecture 37, Pg 1 Physics 1501: Lecture 37 Today’s Agenda l Announcements çHomework...

Physics 1501: Lecture 37, Pg 1

Physics 1501: Lecture 37Physics 1501: Lecture 37TodayToday’’s Agendas Agenda

AnnouncementsHomework #12 (Dec. 9): 2 lowest droppedMidterm 2 … in class WednesdayFriday: review session … bring your questions

Today’s topicsChap.18: Heat and Work

» Zeroth Law of thermodynamics» First Law of thermodynamics and applications» Work and heat engines

Chap.19: Second law of thermodynamics» Efficiency» Entropy


Chap. 18: Work & 1Chap. 18: Work & 1stst Law Law

The Laws of Thermodynamics

0) If two objects are in thermal equilibrium with a third, they are in equilibrium with each other.

1) There is a quantity known as internal energy that in an isolated system always remains the same.

2) There is a quantity known as entropy that in a closed system always remains the same (reversible) or increases (irreversible).


Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics

Thermal equilibrium: when objects in thermal contact cease heat transfersame temperature

T1T2

U1 U2

=

If objects A and B are separately in thermal equilibrium with a third object C, then objects A and B are in

thermal equilibrium with each other.

AC

B


First Law of ThermodynamicsFirst Law of Thermodynamics First Law of Thermodynamics

U = Q + W

variation of internal energyheat flow “in” (+) or “out” (-)

work done “on” the system

Independent of path in PV-diagramDepends only on state of the system (P,V,T, …)Energy conservation statement only U changes


Heat EnginesHeat Engines We now try to do more than just raise the temperature of an

object by adding heat. We want to add heat to get some work done!

Heat engines: Purpose: Convert heat into work using a cyclic process Example: Cycle a piston of gas between hot and cold reservoirs* (Stirling cycle)

1) hold volume fixed, raise temperature by adding heat

2) hold temperature fixed, do work by expansion

3) hold volume fixed, lower temperature by draining heat

4) hold temperature fixed, compress back to original V


Heat EnginesHeat Engines Example: the Stirling cycle

GasT=TH

GasT=TH

GasT=TC

GasT=TC

V

P

TC

TH

Va Vb

1 2

34

We can represent this cycle on a P-V diagram:

11 2

34*reservoir: large body whose temperature does not change when it absorbs or gives up heat


Identify whether Heat is ADDED or REMOVED from the

gas Work is done BY or ON the gas for each

step of the Stirling cycle:

V

P

TC

TH

Va Vb

1 2

34

ADDEDREMOVED

BYON

1

HEAT

WORK

step

ADDEDREMOVED

BYON

2

ADDEDREMOVED

BYON

3

ADDEDREMOVED

BYON

4

Heat EnginesHeat Engines

U = Q + W


Realistic Stirling EnginesRealistic Stirling Engines

beta-type: joined chambers

From Wikipedia

2 typesAlpha-type: 2 separate chambers


Realistic Stirling EnginesRealistic Stirling Engines Alpha-type Most of the working gas is

in contact with the hot cylinder walls, it has been heated and expansion has pushed the hot piston to the bottom of its travel in the cylinder. The expansion continues in the cold cylinder, which is 90° behind the hot piston.

Maximum volume: the hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops.

Most pf the gas is in the cold cylinder and cooling continues. The cold piston, powered by flywheel momentum compresses the remaining part of the gas.

Minimum volume: gas will now expand in the hot cylinder, be heated once more, driving the hot piston in its power stroke.


Realistic Stirling EnginesRealistic Stirling Engines Beta-type:

Power piston (dark grey) has compressed the gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger.

The heated gas increases in pressure and pushes the power piston to the farthest limit of the power stroke.

The displacer piston now moves, shunting the gas to the cold end of the cylinder.

The cooled gas is now compressed by the flywheel momentum. This takes less energy, since when it is cooled its pressure drops.


Another look at beta-typeAnother look at beta-type

“real” one


Chap. 19: Heat Engines and the 2Chap. 19: Heat Engines and the 2ndnd Law of ThermodynamicsLaw of Thermodynamics

A schematic representation of a heat engine. The engine receives energy Qh from the hot reservoir, expels energy Qc to the cold reservoir, and does work W.

If working substance is a gas

Hot reservoir

Cold reservoir

Engine

Qh

Qc

Weng

V

P

Area = Weng

Engine


Heat Engines and the 2Heat Engines and the 2ndnd Law of Law of ThermodynamicsThermodynamics

A heat engine goes through a cycle1st Law gives

U = Q + W =0

So Qnet=|Qh| - |Qc| = -W = Weng

Hot reservoir

Cold reservoir

Engine

Qh

Qc

Weng

Engine


Efficiency of a Heat EngineEfficiency of a Heat Engine

How can we define a “figure of merit” for a heat engine? Define the efficiency as:

It is It is impossibleimpossible to construct a heat engine that, operating to construct a heat engine that, operating in a cycle, produces no other effect than the absorption in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an of energy from a reservoir and the performance of an equal amount of workequal amount of work


Heat Engines and the Second law of Heat Engines and the Second law of ThermodynamicsThermodynamics

Reservoir

Engine

Qh Weng

It is It is impossibleimpossible to to construct a heat engine construct a heat engine that, operating in a cycle, that, operating in a cycle, produces no other effect produces no other effect than the absorption of than the absorption of energy from a reservoir energy from a reservoir and the performance of and the performance of an equal amount of workan equal amount of work

Engine


Consider two heat engines: Engine I:

» Requires Qin = 100 J of heat added to system to get W=10 J of work

Engine II:

» To get W=10 J of work, Qout = 100 J of heat is exhausted to the environment

Compare I, the efficiency of engine I, to II, the efficiency of engine II.

A) I < II B) I > II C) Not enough data to determine

Lecture 37: Act 1Lecture 37: Act 1EfficiencyEfficiency


Reversible/irreversible processesReversible/irreversible processes

Reversible process: Every state along some path is an equilibrium state The system can be returned to its initial conditions along the

same path Irreversible process;

Process which is not reversible !

Most real physical processes are irreversible E.g., energy is lost through friction and the initial conditions

cannot be reached along the same path However, some processes are almost reversible

» If they occur slowly enough (so that system is almost in equilibrium)


The Carnot EngineThe Carnot Engine

No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

A.A. AAB, the gas expands isothermally B, the gas expands isothermally while in contact with a reservoir at Twhile in contact with a reservoir at Thh

B.B. BBC, the gas expands adiabatically C, the gas expands adiabatically (Q=0)(Q=0)

C.C. CCD, the gas is compressed D, the gas is compressed isothermally while in contact with a isothermally while in contact with a reservoir at Treservoir at Tcc

D.D. DDA, the gas compressed A, the gas compressed adiabatically (Q=0)adiabatically (Q=0)

V

P

AB

CD

Weng


The Carnot EngineThe Carnot Engine

All real engines are less efficient than the Carnot engine because they operate irreversibly due to friction as they complete a cycle in a brief time period.

Carnot showed that the thermal efficiency of a Carnot Carnot showed that the thermal efficiency of a Carnot engine is:engine is:


Entropy and the 2Entropy and the 2ndnd Law Law

Consider a reversible process between two equilibrium states The change in entropy S between the two states is given by the energy Qr transferred along the reversible path divided by the absolute temperature T of the system in this interval.

The Second Law of ThermodynamicsThe Second Law of Thermodynamics

““There is a quantity known as There is a quantity known as entropyentropy that in a closed system that in a closed system always remains the same (always remains the same (reversiblereversible) or increases ) or increases ((irreversibleirreversible).).””

Entropy is a measure of disorder in a system.Entropy is a measure of disorder in a system.


Entropy and the 2Entropy and the 2ndnd Law Law What about the following situation

Atoms all located in half the room

Although possible, it is quite improbable

Disorderly arrangements are much more probable than orderly ones

Isolated systems tend toward greater disorder Entropy is a measure of that

disorder Entropy increases in all natural

processes

no atomsall atoms

Physics 1501: Lecture 37, Pg 1 Physics 1501: Lecture 37 Today’s Agenda l Announcements çHomework...

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